The figure comes as Cambridgeshire CC set a cap-busting budget which would demand a £42 increase on its band D council tax.
Oxfordshire CC, the other potential cap-buster among the counties, delayed making a decision at a meeting this week. It is set to consider cap-busting budgets from the Labour and Liberal Democrat groups next Tuesday.
The LGC budget survey shows no other counties are likely to challenge their provisional caps. The figures indicate next year's average county band D bill will be £485. This compares with an increase of 4% in county bills last year.
The survey of provisional budgets, most of which still have to go to full council, show big cuts to spending on services and a heavy reliance on reserves.
Service cuts totalling £200 million are proposed by 18 counties. A total of 26 counties said they would need to use £177m from reserves. The vast majority of counties are expecting to spend at the government-imposed capping limit.
Some of the highest predicted increases in the provisional county bills surveyed by LGC are in the south. The greatest hike being contemplated is in Oxfordshire, which will vote on upping bills by up to 17% at a council meeting in two weeks.
Buckinghamshire, Cambridgeshire, East Sussex and Oxfordshire are all facing increases of 9% or more.
The full picture on council tax bills will not emerge until next month. Districts and metropolitan and London councils do not have to finalise their budgets until 11 March.
Some of the highest increases are predicted in these authorities, which are likely to push the average for England to the 8% predicted by chief secretary to the Treasury William Waldegrave.
Birmingham City Council said this week it is facing an 11% increase in council tax as well as cutting 727 jobs.